"MINKOWSKI PRODUCT OF CONVEX SETS AND PRODUCT NUMERICAL RANGE" by Chi-Kwong Li, Diane Christine Pelejo et al.
 

Document Type

Article

Department/Program

Mathematics

Journal Title

OPERATORS AND MATRICES

Pub Date

Fall 11-4-2016

Volume

10

Issue

4

Abstract

Let K-1, K-2 be two compact convex sets in C. Their Minkowski product is the set K1K2 = {ab : a is an element of K-1, b is an element of K-2}. We show that the set K1K2 is star-haped if K-1 is a line segment or a circular disk. Examples for K-1 and K-2 are given so that K-1 and K-2 are triangles (including interior) and K1K2 is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product numerical range in the study of quantum information science. Additional results and open problems are presented.

DOI

10.7153/oam-10-53

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